Rolling machine element

ABSTRACT

A rolling machine element capable of remarkably increasing a loading capacity, rigidity, and accuracy by forming a crowning based on an oval shape at the raceway surface end part of a guide block (ball guide, roller guide, etc.) or an outer tube (ball spline, ball bush, etc.) to accept a large load on rolling elements even near the end of the crowning. The rolling machine element includes a first member in which a raceway surface is formed and a second member on which the first member is mounted through the rolling elements and which is formed to be able to guide the first member in a specified direction. The rolling machine element is characterized in that the first member can be moved in the guiding direction of the second member by allowing the rolling elements to move in an out of the raceway surface in an orderly arranged state, and the crowning based on the oval shape is formed at the end part of the raceway surface of the first member where an access point for the rolling elements is formed.

TECHNICAL FIELD

The present invention relates to rolling machine elements, such as ballguides, roller guides, ball splines and ball bushes, and in particular,to a rolling machine element whose loading capacity, rigidity andaccuracy are remarkably increased by forming a crowning based on an ovalshape at an end part of a raceway surface of a guide block (ball guide,roller guide, etc.) or an outer tube (ball spline, ball bush, etc.) tomake large load act on rolling members even near the end of thecrowning.

TECHNICAL BACKGRONND

As shown in FIG. 9, a ball guide 1 is formed to allow a guide block 2 tobe movable on a rail 3 in a direction indicated by an arrow A or B. Inthe guide block 2, a large number of balls 4, which is one example ofrolling members, are rolled and circulated in an orderly arranged state.During the rolling and circulation, balls 4 residing within a range of araceway surface length It are made to come into contact with a racewaysurface 3 a of the rail 3 and a raceway surface 2 a of the guide block 2so as to sustain load applied to the guide block 2 from outside.

Roller guides, ball splines, ball bushes and others are also formed toallow rolling members to be rolled and circulated, while there are someelements, such as ball slides and cross roller guides, which do notallow rolling members to circulate therein.

In any of these elements, how a crowning is imparted to both end partsof the raceway surface is so important a factor as to determine allperformances including accuracy in running and duration of life (referto non-patent reference 1).

However, as shown in FIG. 10, a conventional crowning 2 b has a crowninglength X_(r) (a length from a crowing start point “o” to a crowing end“a”) and a crowing relief amount λ_(e), and is based on a circular arc 5whose radius R is decided to make the arc abut on a raceway surface 2 aat the crowning start point “o”. The radius R is expressed by amathematical expression 1 and the circular arc 5 is expressed by amathematical expression 2. $\begin{matrix}{R = \frac{X_{r}^{2} + \lambda_{e}^{2}}{2\quad\lambda_{e}}} & \left\lbrack {{mathematical}\quad{expression}\quad 1} \right\rbrack \\{{x^{2} + \left( {y - R} \right)^{2}} = R^{2}} & \left\lbrack {{mathematical}\quad{expression}\quad 2} \right\rbrack\end{matrix}$

The formation of the circular arc 5 faithfully on the expression resultsin an increase in manufacturing costs. Hence, the circular arc has beenactually formed as shown in FIG. 11 wherein, with the circular arc 5 asa base, an edge ranging from the crowing start point “o” to the point“a” decided by the crowing relief amount λ_(e) at the crowing end 2 c ischamfered linearly, or as shown in FIG. 12 wherein an edge starting fromthe crowing start point “o” is formed into a polygonal shape whoseapexes are points “d”, “c”, “b” and “a” on the circular arc 5.

As shown in FIG. 10, however, in the case of the circular-arc crowning,a crowning relief amount λ_(x), which depends on a distance “x” startingfrom the crowing start point “o”, becomes large while the distance “x”is still small. As a result, it has been that a ratio of load (loadfactor) sustained by the balls 4 positioned on the flat raceway surface2 a to load sustained by the balls 4 residing in the range of thecrowning length X_(r) becomes lower.

This implies that the balls 4 positioned in the range of the racewaysurface length I_(t) are not fully vitalized. In order to raise the loadcapability, rigidity and accuracy, it has been thus necessary to changethe shape of the crowning into shapes other than the circular arc.

Non-patent reference 1: “Research for load distribution andaccuracy/rigidity in a linear motion ball guide system” by ShigeoSHIMIZU, Journal of Japan Society for Precision Engineering, November1992

Non-patent reference 2: “On load rating of a linear motion ball bearing”by Shigeo HIMIZU, Journal of Japanese Society of Tribologists, November1999

Non-patent reference 3: “Dynamic capacity of a linear motion rollingguide element” by Shigeo SHIMIZU, Kosaido Co., Ltd., February 1999

DISCLOSURE OF THE INVENTION Problem to be Solved by the Invention

The present invention has been made in order to remove the drawbacks ofthe conventional art provided above, and has as its object to provide arolling machine element which is provided with a first member formedwith a raceway surface, and a second member to which the first member isattached through rolling members to enable guiding of the first memberto a predetermined direction, and which is so arranged that the rollingmembers are allowed to move in and out of the raceway surface in anorderly arranged state to allow the first member to move in the guidingdirection of the second member, wherein a crowning based on an ovalshape is formed at an end part of the raceway surface of the firstmember, the end part being an access point for the rolling members, sothat a load factor of the rolling members positioned in the range of thecrowning is improved to enhance loading capacity, rigidity and accuracyof the rolling machine element.

Another object is to form, in the arrangement provided above, a crowningbased on an oval shape with a short axis decided by a predeterminedcrowning relief amount at an end part of a raceway surface of a firstmember, the end part being the access point for the rolling members, sothat loading of the rolling members working on the rolling memberspositioned at the end part of the crowning becomes exactly “O” when amaximum radial load defined such as by standards or specifications hasbeen applied, and to enable smooth movement of the rolling members inand out of a loading area of the raceway surface, while maintaining aload factor of the rolling members at a high level.

Still another object is to form, in the arrangement provided above, apolygonal crowning based on an oval shape with a short axis decided by apredetermined crowning relief amount and having a plurality of points asapexes, at an end part of a raceway surface of a first member, so thatprocessing of a crowning is facilitated to reduce manufacturing costs ofa rolling machine element with enhanced loading capacity, rigidity andaccuracy.

Means for Solving the Problem

Briefly, The present invention (claim 1) is to provide a rolling machineelement which is provided with a first member formed with a racewaysurface, and a second member to which the first member is attachedthrough rolling members to enable guiding of the first member to apredetermined direction, and which is so arranged that the rollingmembers are allowed to move in and out of the raceway surface in anorderly arranged state to allow the first member to move in the guidingdirection of the second member, characterized in that a crowning basedon an oval shape is formed at an end part of the raceway surface of thefirst member, the end part serving as an access point for the rollingmembers.

The present invention (claim 2) is to provide a rolling machine elementwhich is provided with a first member formed with a raceway surface, anda second member to which the first member is attached through rollingmembers to enable guiding of the first member to a predetermineddirection, and which is so arranged that the rolling members are allowedto move in and out of the raceway surface in an orderly arranged stateto allow the first member to move in the guiding direction of the secondmember, characterized in that a crowning based on an oval shape with ashort axis decided by a predetermined crowning relief amount is formedat an end part of the raceway surface of the first member, the end partserving as an access point for the rolling members.

The present invention (claim 3) is to provide a rolling machine elementwhich is provided with a first member formed with a raceway surface, anda second member to which the first member is attached through rollingmembers to enable guiding of the first member to a predetermineddirection, and which is so arranged that the rolling members are allowedto move in and out of the raceway surface in an orderly arranged stateto allow the first member to move in the guiding direction of the secondmember, characterized in that a polygonal crowning based on an ovalshape with a short axis decided by a predetermined crowning reliefamount and having a plurality of points as apexes is formed at an endpart of the raceway surface of the first member, the end part serving asan access point for the rolling members.

Effect of the Invention

In a rolling machine element which is provided with a first memberformed with a raceway surface, and a second member to which the firstmember is attached through rolling members to enable guiding of thefirst member to a predetermined direction, and which is so arranged thatthe rolling members are allowed to move in and out of the racewaysurface in an orderly arranged state to allow the first member to movein the guiding direction of the second member, a crowning based on anoval shape is formed at an end part of the raceway surface of the firstmember, the end part serving as an access point for the rolling members.Thus, the present invention can enhance a load factor of the rollingmembers positioned within a range of the crowning, whereby providing anadvantage of enhancing loading capacity, rigidity and accuracy of therolling machine element.

In the arrangement provided above, a crowning based on an oval shapewith a short axis decided by a predetermined crowning relief amount isformed at an end part of the raceway surface of the first member, theend part serving as an access point for the rolling members.Accordingly, the present invention provides an advantage of allowing theloading of the rolling members working on the rolling members positionedat the end of the crowning to be exactly “0” when a maximum radial loaddefined such as by standards or specifications has been applied. Also,smooth movement of the rolling members in and out of a loading area ofthe raceway surface is ensured, while maintaining a load factor of therolling members at a high level.

Further, in the arrangement provided above, a polygonal crowning basedon an oval shape with a short axis decided by a predetermined crowningrelief amount and having a plurality of points as apexes is formed atthe end part of the raceway surface of the first member. Thus, thepresent invention may provide an advantage of facilitating processing ofthe crowning to reduce manufacturing costs of the rolling machineelement with enhanced loading capacity, rigidity and accuracy.

PREFERRED EMBODIMENTS OF THE INVENTION

The present invention is hereinafter described based on some embodimentsshown in the drawings. A rolling machine element 10 according to a firstembodiment of the present invention is a ball guide, for example, asshown in FIG. 1, which is provided with a guide block 11, an example ofa first member, formed with a raceway surface 14, and provided with arail 12, an example of a second member, to which the guide block 11 isattached through balls 13, an example of rolling members, to enableguiding of the guide block 11 in a predetermined direction, and which isso arranged that the balls 13 move in and out of the raceway surface 14of the guide block 11 in an orderly arranged state to allow the guideblock 11 to move in the guiding direction of the rail 12. In the rollingmachine element 10, a crowning 14 a based on an oval shape 15 with ashort axis decided by a predetermined crowning relief amount λ_(e), isformed at an end part, or an access point for the balls 13, of theraceway surface 14 of the guide block 11.

With a crowning start point “o” as an origin, a direction along theraceway surface 14 as an x-axis, and a direction along a height of theguide block 11 as a y-axis, an equation of the oval shape 15 isexpressed by the following mathematical expression 3: $\begin{matrix}{{{\left( \frac{x}{X_{r}} \right)^{2} + \left( \frac{y}{\lambda_{e}} \right)^{2}} = 1},} & \left\lbrack {{mathematical}\quad{expression}\quad 3} \right\rbrack\end{matrix}$where X_(r) is a long axis (crowning relief width) and λ_(e) is a shortaxis (crowning relief amount).

When a length of the crowning relief width X_(r), which may be set atany value, is extended to substantially a center of the raceway surface14, substantially all range of a raceway length l_(t) is in a state ofcrowning, which is a so-called full-crowning state. Therefore, it isconsidered that rigidity and life duration are deteriorated but thatguiding accuracy is remarkably improved and abrasion resistance isdramatically reduced.

For comparison with the conventional circular-arc crowning, a circulararc 16 of a radius R connecting the crowning start point “o” and acrowning end “a” is indicated in FIG. 1. However, comparing the crowning14 a based on the oval shape 15 with the circular arc 16, the positionsof the crowning start point “o” and the crowning end “a” are common, butthe crowning 14 a is more largely arched toward the direction of theorigin of the y-axis. This largely arched portion ensures improvement inthe load factor of the balls 13.

A rolling machine element 20 according to a second embodiment of thepresent invention is a ball guide, for example, as shown in FIGS. 2 to4, which is provided with a guide block 21, an example of a firstmember, formed with a raceway surface 24, and provided with a rail 22,an example of a second member, to which the guide block 21 is attachedthrough balls 13, an example of rolling members, to enable guiding ofthe guide block 21 in a predetermined direction, and which is soarranged that the balls 13 move in and out of the raceway surface 24 ofthe guide block 21 in an orderly arranged state to allow the guide block21 to move in the guiding direction of the rail 22. In the rollingmachine element 20, a crowning 24 a of a polygonal shape is formed at anend part, or an access point for the balls 13, of the raceway surface 24of the guide block 21, the polygonal shape being based on an oval shape15 with a short axis decided by a predetermined crowning relief amountλ_(e) and having a plurality of points a, b, c and o as apexes.

The oval shape 15, which is the base of the crowning 24, is similar tothe first embodiment of the present invention. The apexes are notlimited to the four points a, b, c and o, but may more or less than thisnumber.

Since the rolling machine element 20 is a ball guide, for example, anend plate 25 is attached to both ends of the guide block 11, as shown inFIG. 4. By allowing the balls 13 to pass through the end plates 25, theballs 13 are adapted to roll and circulate through the guide block 11.

The present invention is arranged as described above. Hereinafter aredescribed the effects of the present invention. The explanation providedbelow is on the effects of the guide block 21 in the rolling machineelement 20 according to the second embodiment of the present invention.As shown in FIG. 4, the balls 13 are interposed between the guide block21 and the rail 22, so that the guide block 21 can be freely moved withrespect to the fixed rail 22 in the guiding direction, or a directionindicated by an arrow C or an arrow D, of the rail 22. At this time, theballs 13 roll and circulate in the guide block 21 in a directionindicated by an arrow G or an arrow H.

In case a radial load F which is ½ of a basic dynamic load rating workson the guide block 21, a deformation amount equivalent to the crowningrelief amount λ_(e) is caused between the raceway surface 24, the balls13 and the rail 22, as far as the raceway surface 24 other than thecrowning 24 a is concerned.

Once the balls 13 move on in the direction of the arrow H and enter thearea of the crowning 24 a, as the balls 13 come closer to an end of thecrowning, the ball loading is reduced. By the time the balls 13 havereached an end of the crowning, the ball loading has been reduced toexactly “0”, and then, the balls 13 keep moving on in the direction ofthe arrow H. The reason why the ball loading becomes exactly “0” at thecrowning end is that the guide block 11 descends by the crowning reliefamount λ_(e) due to the radial load F and that a gap between the racewaysurface 24 and the rail 22 at the crowning end becomes equal to adiameter of each of the balls.

Contrarily, once the balls 13 move on in the direction of the arrow Gand have reached the crowning end, the ball loading is “0” which,however, increases as the balls 13 further advance, and becomes maximumat the crowning start point. The balls 13 then keep further rollingalong the raceway surface 24. At this time, a deformation amount betweenthe raceway surface 24, the balls 13 and the rail 22 is equal to thecrowning relief amount X_(e).

A life duration formula defined by the International Organization forStandardization (ISO) is applied under a radial load of equal to or lessthan ½ of a basic dynamic load rating which is also determined by aformula agreed upon by the ISO.

Accordingly, by providing the crowning relief amount λ_(e) equivalent toa deformation amount of the balls under the radial load which is ½ ofthe basic dynamic load rating, the entire raceway surface 24 includingthe crowning 24 a is brought into contact with the balls 13 even whenthe radial load is working on to thereby obtain a sufficient loadingcapacity. Further, since the gap between the raceway surface 24 and therail 22 at the crowning end becomes equal to the diameter of each of theballs 13, the balls 13 can smoothly move in or out of the racewaysurface 24.

Table 1 indicates examples of calculation in case the crowning of theball guide is a circular-arc crowning, a parabolic crowning and an ovalcrowning. The calculation has been carried out with the followingrequirements: ball diameter Dw=6.35 mm, crowning relief amountλ_(e)=0.023228 mm, pertinency factor f (=raceway surface radius R/balldiameter D_(w))=0.52, and radius R=867.983 mm of a circle of thecircular-arc crowning, and on the assumption that the radial load Fwhich is ½ of a basic dynamic load rating C works on. TABLE 1circular-arc/parabolic crowning oval crowning x/X_(r) λ_(x) mm (1 −λ_(x)/λ_(e))^(1.5) λ_(x) mm (1 − λ_(x)/λ_(e))^(1.5) 0.000 0.000 1.0000.000 1.000 0.100 0.232 0.985 0.116 0.992 0.200 0.929 0.941 0.469 0.9700.300 2.090 0.868 1.070 0.932 0.400 3.716 0.770 1.939 0.877 0.500 5.8070.650 3.112 0.806 0.600 8.362 0.512 4.646 0.716 0.700 11.382 0.364 6.6400.604 0.800 14.866 0.216 9.291 0.465 0.850 16.782 0.146 10.992 0.3820.900 18.815 0.083 13.103 0.288 0.950 20.963 0.030 15.975 0.174 0.97522.081 0.011 18.067 0.105 0.990 22.766 0.003 19.951 0.053 1.000 23.2280.000 23.228 0.000

In Table 1, the first column indicates a ratio of a distance in thedirection of the x-axis from the crowning start point “o” to the longaxis X_(r) (crowning width) of the oval shape 15 indicated in FIG. 1,i.e. a dimensionless quantity. The second and the third columns indicatecases of the circular-arc crowning and the parabolic crowning of theconventional art, and the fourth and the fifth columns indicate cases ofthe oval crowning of the present invention. The second and the fourthcolumns indicate a distance λ_(x) in the direction of the y-axis fromthe crowning start point “o”, and the third and the fifth columnsindicate a load factor (1−(1−λ_(x)/λ_(e))^(1.5)) of the balls. Thecircular-arc crowning and the parabolic crowning each being a quadraticexpression, match in the distance λ_(x) within a range of significantdigits and also match in the load factor, and thus are indicated in thesame columns.

The load factor is a ratio of a ball loading when the balls arepositioned at the crowning portion to a ball loading when the balls arepositioned at the raceway surface other than the crowning portion.Specifically, the ball loading at the crowning start point “o” is “1”and at the crowning end “a” is “0”, the load factor resulting in “0”.

As can be seen from Table 1, when the crowning width x/X_(r)=0.5, theload factor of the oval crowning is 80.6%, which is higher than the loadfactor 65% of the circular-arc crowning and the parabolic crowning. Thisis comparatively indicated in the diagrams of FIG. 5.

Indicated by (1) is the case of the circular-arc crowning, and by (2) isthe case of the oval crowning. The lower diagram whose vertical axisindicating the distance λ_(x) shows the shapes of the crownings as theyare. It can be seen that the oval crowning is more largely archeddownward by the hatched area than the circular-arc crowning.

Also, as can be seen from the upper diagram whose vertical axisindicating the load factor, the load factor of the oval crowning ishigher by the hatched area than that of the circular-arc crowning.

In the diagrams shown in FIG. 6, the horizontal axes show the pertinencyfactor, while the vertical axes indicating the basic dynamic load ratingC, a ball loading Q_(c) when the radial load which is ½ of the basicdynamic load rating C works on, the crowning relief amount λ_(e), adeformation amount δ_(Qc) when the ball loading Q_(c) works on, amaximum Hertzian stress σ_(max), and a ball diameter D_(w)/crowningrelief amount λ_(e). The requirements for calculation are: racewaysurface length I_(t)=72 mm, ball diameter D_(w)=6.35 mm, number of rowsof the balls i_(t)=2 rows, and contact angle α=45°. The contact angleα=45° implies that the balls and the raceway surface abut with eachother being inclined by 45° with respect to the direction on which theradial load works on.

As can be seen from the lowermost diagram of FIG. 6, the ratio of theball diameter D_(w) and the crowning relief amount λ_(e) varies from 270to 290 with respect to the variation of the pertinency factor f=0.51 to0.55.

Table 2 shows some examples of calculation associated with the crowningsin case the rolling machine element 10 is a roller guide. Thecalculation has been carried out under the following requirements: aroller diameter D_(w)=6.35 mm, a roller length L_(w)=6.35 mm, thecrowning relief amount λ_(e)=0.016829 mm, a roller effective lengthfactor f_(L)=0.7 (=roller effective length L_(we)/roller length L_(w)),and a radius R=1198.015 mm of a circle in the circular-arc crowning, andon the assumption that a radial load F which is ½ of the basic dynamicload rating C works on. TABLE 2 circular-arc/parabolic crowning ovalcrowning x/X_(r) λ_(x) mm (1 − λ_(x)/λ_(e))^(10/9) λ_(x) mm (1 −λ_(x)/λ_(e))^(10/9) 0.000 0.000 1.000 0.000 1.000 0.100 0.168 0.9890.084 0.994 0.200 0.673 0.956 0.340 0.978 0.300 1.515 0.901 0.775 0.9490.400 2.693 0.824 1.405 0.908 0.500 4.207 0.726 2.255 0.852 0.600 6.0580.609 3.366 0.780 0.700 8.246 0.473 4.811 0.688 0.800 10.771 0.321 6.7320.567 0.850 12.159 0.241 7.964 0.491 0.900 13.631 0.158 9.493 0.3970.950 15.188 0.075 11.574 0.274 0.975 15.998 0.035 13.090 0.188 0.99016.494 0.013 14.455 0.113 1.000 16.829 0.000 16.829 0.000

In Table 2, each of the columns indicates the same items as in Table 1.As can be seen from Table 2, when the crowning width x/X_(r)=0.5, theload factor of the oval crowning is 85.2%, which is again higher than72.6% of the circular-arc crowning and the parabolic crowning. This iscomparatively indicated in the diagrams of FIG. 7.

As in FIG. 5, indicated by (1) is the case of the circular-arc crowning,and by (2) is the case of the oval crowning. The lower diagram whosevertical axis indicating the distance λ_(x) shows the shapes of thecrownings as they are. It can be seen that the oval crowning is morelargely arched downward by the hatched area than the circular-arccrowning.

Also, as can be seen from the upper diagram whose vertical axisindicating the load factor, the load factor of the oval crowning ishigher by the hatched area than that of the circular-arc crowning.

In the diagrams shown in FIG. 8, the horizontal axes show a rollereffective length factor f_(L), while the vertical axes indicating thebasic dynamic load rating C, a ball loading Q_(c) when the radial loadwhich is ½ of the basic dynamic load rating C works on, the crowningrelief amount λ_(e), a deformation amount δ_(Qc) when the ball loadingQ_(c) works on, a maximum Hertzian stress σ_(max), and a ball diameterD_(w)/crowning relief amount λ_(e). The requirements for calculationare: raceway surface length l_(t)=72 mm, roller diameter D_(w)=6.35 mm,number of rows of the balls i_(t)=2 rows, and contact angle α=45°.

As can be seen from the lowermost diagram of FIG. 6, the ratio of theball diameter D_(w) and the crowning relief amount λ_(e) varies from 330to 460 with respect to the variation of the roller effective lengthfactor f_(L)=0.6 to 0.9.

In the embodiments provided above, the roller machine elements 10 and 20have each been described as a ball guide. However, the present inventionis not limited to this, but the roller machine element may, for example,be a roller guide, a ball spline and a ball bush. The guiding by a railor a shaft is not limited to a direction along a linear line, but may bealong a curved line provided by a curved rail such as an R guide.

The rolling members are not limited to balls but may be any roller, suchas a cylindrical roller, a needle roller, a barrel roller or a conicalroller. In addition, the rolling members are not limited to those whichare rolled and circulated in a guide block or an outer cylinder, but maybe ones which are rotatably attached such as to a rail or a retainer,e.g. a cross roller guide or a ball slide.

Where the roller members are arranged to abut on the guide block and therail at a certain contact angle, the crowning relief amount λ_(e) may bedetermined according to an elastic deformation amount of the rollermembers in the direction of the contact angle.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a partial longitudinal sectional view showing the shape andmathematical expressions associated with an oval crowing in a rollingmachine element according to a first embodiment of the presentinvention;

FIG. 2 is a partial longitudinal sectional view showing an enlargedcrowning portion of the rolling machine element shown in FIG. 2, inwhich FIGS. 2 to 4 show a second embodiment of the present invention;

FIG. 3 is a side view showing the rolling element, which indicates acrowning at both ends of a raceway surface of a guide block, balls and arail, as well as a state illustrated in an exaggerated manner where theguide block has come down due to the deformation of the balls, which isascribed to radial load that has worked on the guide block:

FIG. 4 is a partial longitudinal sectional view showing a state wherethe balls move on the rail, rolling and circulating in the guide blockunder the radial load;

FIG. 5 illustrates diagrams showing results of calculation of crowningshapes and load factors of a ball guide;

FIG. 6 illustrates diagrams showing a pertinency factor, as well as abasic dynamic load rating, a ball loading, a crowning relief amount, aball deformation amount, a maximum Hertzian stress, and a ratio of aball diameter to a crowning relief amount of the ball guide;

FIG. 7 illustrates diagrams showing results of calculation of crowningshapes and load factors of a roller guide;

FIG. 8 illustrates diagrams showing a pertinency factor, as well as abasic dynamic load rating, a ball loading, a crowning relief amount, aball deformation amount, a maximrnm Hertzian stress, and a ratio of aball diameter to a crowning relief amount of the roller guide;

FIG. 9 is a longitudinal sectional view showing a ball guide, in whichFIGS. 9 to 12 show conventional examples;

FIG. 10 is a partial longitudinal sectional view showing an enlargedshape and mathematical expressions associated with a circular-arccrowning;

FIG. 11 is a longitudinal sectional view showing a crowning based on acircular arc formed by linearly chamfering between a crowning startpoint and a crowning end; and

FIG. 12 is a longitudinal sectional view showing a polygonal crowningbased on a circular arc formed by sequentially connecting a plurality ofpoints on a circular arc between a crowning start point and a crowningend.

DESCRIPTION OF SYMBOLS

10 rolling machine element

11 guide block as an example of a first member

12 rail as an example of a second member

13 balls as an example of rolling members

14 raceway surface

14 a crowning

15 oval shape

20 rolling machine element

21 guide block as an example of a first member

22 rail as an example of a second member

23 raceway surface

24 a crowning

1. A rolling machine element which is provided with a first memberformed with a raceway surface along which rolling members roll under aload, and a second member to which said first member is attached throughthe rolling members to enable guiding of said first member to apredetermined direction, and which is so arranged that said rollingmembers are allowed to move in and out of said raceway surface in anorderly arranged state to allow said first member to move in the guidingdirection of said second member, characterized in that a crowning ofoval shape (except for circular-arc shape) is formed at an end part ofthe raceway surface of said first member, the end part serving as anaccess point for said rolling members.
 2. A rolling machine elementwhich is provided with a first member formed with a raceway surfacealong which rolling members roll under a load, and a second member towhich said first member is attached through the rolling members toenable guiding of said first member to a predetermined direction, andwhich is so arranged that said rolling members are allowed to move inand out of said raceway surface in an orderly arranged state to allowsaid first member to move in the guiding direction of said secondmember, characterized in that a crowning of oval shape (except forcircular-arc shape) with ½ of a short axis decided by a predeterminedcrowning relief amount is formed at an end part of the raceway surfaceof said first member, the end part serving as an access point for saidrolling members.
 3. A rolling machine element which is provided with afirst member formed with a raceway surface along which rolling membersroll under a load, and a second member to which said first member isattached through the rolling members to enable guiding of said firstmember to a predetermined direction, and which is so arranged that saidrolling members are allowed to move in and out of said raceway surfacein an orderly arranged state to allow said first member to move in theguiding direction of said second member, characterized in that apolygonal crowning based on an oval shape (except for a circular-arcshape) with ½ of a short axis decided by a predetermined crowning reliefamount, having a plurality of points as apexes and guiding the rollingmembers to roll under the load is formed at an end part of the racewaysurface of said first member, the end part serving as an access pointfor said rolling members.
 4. A rolling machine element which is providedwith a first member formed with a raceway surface along which rollingmembers roll under a load, and a second member to which said firstmember is attached through the rolling members to enable guiding of saidfirst member to a predetermined direction, and which is so arranged thatsaid rolling members are allowed to move in and out of said racewaysurface in an orderly arranged state to allow said first member to movein the guiding direction of said second member, characterized in that apolygonal crowning based on an oval shape (except for a circular-arcshape), having a plurality of points as apexes and guiding the rollingmembers to roll under the load is formed at an end part of the racewaysurface of said first member, the end part serving as an access pointfor said rolling members.